I live in Houston and often have trouble showing guests around town. This isn't a touristy place unless you're into museums which are excellent, restaurants which are plentiful, or titty bars (we are famous for them, go figure) Most of Houston didn't exist before 1970, so there isn't much in the line of history. Not much in Galveston either aside from Moody Gardens and the Strand. Corpus is a tiny port town. It does have the Salena statue if you know who she was.
The hill country is beautiful. If you do anything, be sure to see the Texas Museum in Austin, along with the funky night life. San Antonio; The Alamo and the rest of the missions are cool. The riverwalk is good also. Fredericksburg is a charming touristy small town.
Pie Town New Mexico might be on your way ?
